{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:MIWB3TRQ7XJ2VN3AKJ6P7GUPDT","short_pith_number":"pith:MIWB3TRQ","canonical_record":{"source":{"id":"2212.12567","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2022-12-23T19:45:25Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"7d5af6a0604856005b13185b251e66b1419a5a903dfcfb814b620a13d92f03e0","abstract_canon_sha256":"4db811c85e26b43b6b287123af898affb8988c8eb28ea487bed76479894b5ab6"},"schema_version":"1.0"},"canonical_sha256":"622c1dce30fdd3aab760527cff9a8f1cff1dde893898dc99dcdfb9f9443fbd6f","source":{"kind":"arxiv","id":"2212.12567","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2212.12567","created_at":"2026-07-05T05:42:02Z"},{"alias_kind":"arxiv_version","alias_value":"2212.12567v2","created_at":"2026-07-05T05:42:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2212.12567","created_at":"2026-07-05T05:42:02Z"},{"alias_kind":"pith_short_12","alias_value":"MIWB3TRQ7XJ2","created_at":"2026-07-05T05:42:02Z"},{"alias_kind":"pith_short_16","alias_value":"MIWB3TRQ7XJ2VN3A","created_at":"2026-07-05T05:42:02Z"},{"alias_kind":"pith_short_8","alias_value":"MIWB3TRQ","created_at":"2026-07-05T05:42:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:MIWB3TRQ7XJ2VN3AKJ6P7GUPDT","target":"record","payload":{"canonical_record":{"source":{"id":"2212.12567","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2022-12-23T19:45:25Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"7d5af6a0604856005b13185b251e66b1419a5a903dfcfb814b620a13d92f03e0","abstract_canon_sha256":"4db811c85e26b43b6b287123af898affb8988c8eb28ea487bed76479894b5ab6"},"schema_version":"1.0"},"canonical_sha256":"622c1dce30fdd3aab760527cff9a8f1cff1dde893898dc99dcdfb9f9443fbd6f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:42:02.425790Z","signature_b64":"j9fzaHwmbXtzQ/HHQdoRcLKfCE1pKxWhoP26XJ0XfqEBscMgI3BoLK5FGA2cSAK2s/K2IUdhxynhN+qos+eXBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"622c1dce30fdd3aab760527cff9a8f1cff1dde893898dc99dcdfb9f9443fbd6f","last_reissued_at":"2026-07-05T05:42:02.425234Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:42:02.425234Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2212.12567","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T05:42:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qjBLXidGngax2gZuIgrCKQ7epcnxmTSXay7D9cdKf80Anc1ySCkkBYwcIdjXE+3mkNNZ6MraZbL8NxF2M9OXBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T12:37:04.779792Z"},"content_sha256":"8d5e29cb7bdc75edd33ef4c0e1bd8edaafd0edcc517f9c005594204d80379e3d","schema_version":"1.0","event_id":"sha256:8d5e29cb7bdc75edd33ef4c0e1bd8edaafd0edcc517f9c005594204d80379e3d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:MIWB3TRQ7XJ2VN3AKJ6P7GUPDT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Adapting to game trees in zero-sum imperfect information games","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"C\\^ome Fiegel, Michal Valko, Pierre M\\'enard, R\\'emi Munos, Tadashi Kozuno, Vianney Perchet","submitted_at":"2022-12-23T19:45:25Z","abstract_excerpt":"Imperfect information games (IIG) are games in which each player only partially observes the current game state. We study how to learn $\\epsilon$-optimal strategies in a zero-sum IIG through self-play with trajectory feedback. We give a problem-independent lower bound $\\widetilde{\\mathcal{O}}(H(A_{\\mathcal{X}}+B_{\\mathcal{Y}})/\\epsilon^2)$ on the required number of realizations to learn these strategies with high probability, where $H$ is the length of the game, $A_{\\mathcal{X}}$ and $B_{\\mathcal{Y}}$ are the total number of actions for the two players. We also propose two Follow the Regulariz"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.12567","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2212.12567/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T05:42:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ImZN1fJ6sZhX/Ozc5UNUKgpqKuD6rIE0b7b06NmbVkGqU6G6kvYO7o7EU+Hogz7n8eBMf96wmlvzNJY9X50LAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T12:37:04.780423Z"},"content_sha256":"e47ea9d75a82badbdb7804e62ab69417ff6d5ba03c0485702c5da002f5e93fe3","schema_version":"1.0","event_id":"sha256:e47ea9d75a82badbdb7804e62ab69417ff6d5ba03c0485702c5da002f5e93fe3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MIWB3TRQ7XJ2VN3AKJ6P7GUPDT/bundle.json","state_url":"https://pith.science/pith/MIWB3TRQ7XJ2VN3AKJ6P7GUPDT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MIWB3TRQ7XJ2VN3AKJ6P7GUPDT/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-05T12:37:04Z","links":{"resolver":"https://pith.science/pith/MIWB3TRQ7XJ2VN3AKJ6P7GUPDT","bundle":"https://pith.science/pith/MIWB3TRQ7XJ2VN3AKJ6P7GUPDT/bundle.json","state":"https://pith.science/pith/MIWB3TRQ7XJ2VN3AKJ6P7GUPDT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MIWB3TRQ7XJ2VN3AKJ6P7GUPDT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:MIWB3TRQ7XJ2VN3AKJ6P7GUPDT","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"4db811c85e26b43b6b287123af898affb8988c8eb28ea487bed76479894b5ab6","cross_cats_sorted":["cs.LG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2022-12-23T19:45:25Z","title_canon_sha256":"7d5af6a0604856005b13185b251e66b1419a5a903dfcfb814b620a13d92f03e0"},"schema_version":"1.0","source":{"id":"2212.12567","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2212.12567","created_at":"2026-07-05T05:42:02Z"},{"alias_kind":"arxiv_version","alias_value":"2212.12567v2","created_at":"2026-07-05T05:42:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2212.12567","created_at":"2026-07-05T05:42:02Z"},{"alias_kind":"pith_short_12","alias_value":"MIWB3TRQ7XJ2","created_at":"2026-07-05T05:42:02Z"},{"alias_kind":"pith_short_16","alias_value":"MIWB3TRQ7XJ2VN3A","created_at":"2026-07-05T05:42:02Z"},{"alias_kind":"pith_short_8","alias_value":"MIWB3TRQ","created_at":"2026-07-05T05:42:02Z"}],"graph_snapshots":[{"event_id":"sha256:e47ea9d75a82badbdb7804e62ab69417ff6d5ba03c0485702c5da002f5e93fe3","target":"graph","created_at":"2026-07-05T05:42:02Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2212.12567/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Imperfect information games (IIG) are games in which each player only partially observes the current game state. We study how to learn $\\epsilon$-optimal strategies in a zero-sum IIG through self-play with trajectory feedback. We give a problem-independent lower bound $\\widetilde{\\mathcal{O}}(H(A_{\\mathcal{X}}+B_{\\mathcal{Y}})/\\epsilon^2)$ on the required number of realizations to learn these strategies with high probability, where $H$ is the length of the game, $A_{\\mathcal{X}}$ and $B_{\\mathcal{Y}}$ are the total number of actions for the two players. We also propose two Follow the Regulariz","authors_text":"C\\^ome Fiegel, Michal Valko, Pierre M\\'enard, R\\'emi Munos, Tadashi Kozuno, Vianney Perchet","cross_cats":["cs.LG"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2022-12-23T19:45:25Z","title":"Adapting to game trees in zero-sum imperfect information games"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.12567","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:8d5e29cb7bdc75edd33ef4c0e1bd8edaafd0edcc517f9c005594204d80379e3d","target":"record","created_at":"2026-07-05T05:42:02Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"4db811c85e26b43b6b287123af898affb8988c8eb28ea487bed76479894b5ab6","cross_cats_sorted":["cs.LG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2022-12-23T19:45:25Z","title_canon_sha256":"7d5af6a0604856005b13185b251e66b1419a5a903dfcfb814b620a13d92f03e0"},"schema_version":"1.0","source":{"id":"2212.12567","kind":"arxiv","version":2}},"canonical_sha256":"622c1dce30fdd3aab760527cff9a8f1cff1dde893898dc99dcdfb9f9443fbd6f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"622c1dce30fdd3aab760527cff9a8f1cff1dde893898dc99dcdfb9f9443fbd6f","first_computed_at":"2026-07-05T05:42:02.425234Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:42:02.425234Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"j9fzaHwmbXtzQ/HHQdoRcLKfCE1pKxWhoP26XJ0XfqEBscMgI3BoLK5FGA2cSAK2s/K2IUdhxynhN+qos+eXBA==","signature_status":"signed_v1","signed_at":"2026-07-05T05:42:02.425790Z","signed_message":"canonical_sha256_bytes"},"source_id":"2212.12567","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8d5e29cb7bdc75edd33ef4c0e1bd8edaafd0edcc517f9c005594204d80379e3d","sha256:e47ea9d75a82badbdb7804e62ab69417ff6d5ba03c0485702c5da002f5e93fe3"],"state_sha256":"42f8d9b8bbca6ee487368e2f6d0b90c055c7cbb93bc2f92c0ca453ec73676f27"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eUIzZS5BEmfyP9YcxjU30CiahFejKqhQA+twebBHSb4Cf0yydTezhtZ5N1UrGamgvGMAdXPQyZ0xfzquGS7DDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T12:37:04.786405Z","bundle_sha256":"2b031cb72fc635466ade8fc84a3293d5a42ac445a5a31b46e27db064d06ca6c9"}}